
We again apply \(\mathbf {vec}(\mathbf {A}\mathbf {B}\mathbf {C}) = (\mathbf {C}^\top \otimes \mathbf {A})\mathbf {vec}(\mathbf {B})\)  [1]} and maximize over \(\mathbf {vec}(\mathbf {W}_1)\)  to obtain
\(p_{MM}^* &= -\max _{\mathbf {V}_i} \sum _{i=1}^n \mathcal {L}^* \left( \mathbf {V}_i, \mathbf {Y}_i \right)\\&\mbox{s.t. } \Vert  \sum _{i=1}^n {\mathbf {X}}_i^\top \otimes \mathbf {V}_i^\top \Vert _2\le \beta .\) 
